Finite Temperature Time-Dependent Effective Theory For The Goldstone Field In A BCS Superconductor

We extend to finite temperature the time-dependent effective theory for the Goldstone field (the phase of the pair field) θ which is appropriate for superconductors containing one species of charge carrier, described by the BCS Lagrangian. We show that, when Landau damping is neglected, the effective theory can be written as a local time-dependent nonlinear Schrödinger Lagrangian (TDNLSL) which preserves the Galilean invariance of the zero temperature effective theory and is identified with the superfluid component. We then calculate the relevant Landau terms which are non-local and which destroy the Galilean invariance. We show that the retarded θ-propagator (in momentum space) can be well represented by two poles in the lower-half frequency plane, describing damping with a predicted T and |q|dependence. It is argued that the real parts of the Landau terms can be approximately interpreted as contributing to the normal fluid component. E-mail address: [email protected] E-mail address: [email protected] E-mail address: [email protected]